Q52

Given a language $L$, define $L^i$ as follows:

$$L^0 = \{ \varepsilon \}$$ $$L^i = L^{i-1} \bullet L \text{ for all } I >0$$

The order of a language $L$ is defined as the smallest $k$ such that $L^k = L^{k+1}$. Consider the language $L_1 ($over alphabet $0)$ accepted by the following automaton.

The order of $L_1$ is ________.